Concentrated N-dimensional AMM with Polar Coordinates in Rust

ArXiv ID: 2510.05428 “View on arXiv”

Authors: Vasily Tolstikov, Marcus Wentz, Joseph Schiarizzi, Derek Ding

Abstract

We expand on the recent development of n-dimensional automated market makers for stablecoins by showing a way to build concentrated liquidity positions with ticks in polar coordinates in Rust, including the featured ability to skew said concentrated liquidity. We highlight the risk of stacking too many stablecoin pools and how to hedge said risk.

Keywords: Automated Market Makers (AMM), Stablecoins, Liquidity Concentration, DeFi, Rust Programming, Cryptocurrency/DeFi

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring complex n-dimensional invariants, superelliptical shapes, polar coordinate transformations, and extensive derivations, but it lacks backtests, real-world data validation, or concrete implementation results beyond a single Rust code snippet.

  flowchart TD
    A["Research Goal:<br>n-dimensional AMM with<br>concentrated polar liquidity in Rust"] --> B["Key Methodology:<br>Map Cartesian to Polar Coordinates"]
    B --> C["Data & Inputs:<br>Stablecoin Pairs,<br>Liquidity Ranges, Tick Spacing"]
    C --> D["Computational Process:<br>Rust Implementation<br>for Concentration & Skewing"]
    D --> E["Key Findings:<br>Skewed Liquidity Positions &<br>Risk Hedging Strategies"]